Transparent model does not render correctly, looks ok while editing texture
In the Properties window, go to the Material Properties tab. Scroll down to Settings and change the Blend Mode form Opaque to Alpha Blend (or possibly Alphas Clip or Alpha Hashed, depending on your preference).
It is the same for EEVEE and Cycles.
However, take care not to confuse the aforementioned Settings with the Settings under Viewport Display that are available in Cycles, since they only affect the 3D Viewport and not the render.